मान लीजिए f : R → R एक फलन है जिसका व्युत्क्रम x+53 है। तो f(x) किसके बराबर है?

  1. f(x) = 3x + 5
  2. f(x) = 3x - 5
  3. f(x) = 5x - 3
  4. f(x) = 5 - 3x
  5. f(x) मौजूद नहीं है। 

Answer (Detailed Solution Below)

Option 2 : f(x) = 3x - 5
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Detailed Solution

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संकल्पना:

यदि y = f(x) है, तो x = f-1 (y) है। 

गणना:

दिया गया है, f : R → R एक फलन है जिसका व्युत्क्रम x+53 है।

⇒ y = f-1 (x) =x+53

⇒ 3y = x + 5

⇒ x = 3y - 5

⇒y = f-1 (x) 

⇒ x = f(y)

⇒ x = 3y - 5 = f(y)

⇒ f(y) = 3y - 5

⇒f(x) = 3x - 5

अतः माना कि f : R → R एक फलन है जिसका व्युत्क्रम x+53 है, तो f(x) = 3x - 5 है। 

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